Mammalian chromatin is the site of both RNA polymerase II (Pol II) transcription and coupled RNA processing. However, molecular details of such co-transcriptional mechanisms remain obscure, partly because of technical limitations in purifying authentic nascent transcripts. We present a new approach to characterize nascent RNA, called polymerase intact nascent transcript (POINT) technology. This three-pronged methodology maps nascent RNA 5′ ends (POINT-5), establishes the kinetics of co-transcriptional splicing patterns (POINT-nano), and profiles whole transcription units (POINT-seq). In particular, we show by depletion of the nuclear exonuclease Xrn2 that this activity acts selectively on cleaved 5′ P-RNA at polyadenylation sites. Furthermore, POINT-nano reveals that co-transcriptional splicing either occurs immediately after splice site transcription or is delayed until Pol II transcribes downstream sequences. Finally, we connect RNA cleavage and splicing with either premature or full-length transcript termination. We anticipate that POINT technology will afford full dissection of the complexity of co-transcriptional RNA processing. Display omitted •POINT methodology dissects intact nascent RNA processing•Specificity of Xrn2 exonuclease in co-transcriptional RNA degradation•Splicing suppresses Xrn2-dependent premature termination•Different kinetic classes of co-transcriptional splicing in human genes Sousa-Luís et al. describe tripartite methodology to purify and sequence RNA polymerase II-associated intact nascent transcripts (POINT) from mammalian genomes. POINT-5 distinguishes nascent RNA 5′ end caps from 5′ end cleavage, POINT-seq profiles full-length transcription units, and POINT-nano determines the kinetics of co-transcriptional splicing at a single-molecule level.